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Zbl 1072.65025
Gil, Amparo; Segura, Javier; Temme, Nico M.
Algorithm 831: Modified Bessel functions of imaginary order and positive argument. (English)
[J] ACM Trans. Math. Softw. 30, No. 2, 159-164 (2004). ISSN 0098-3500

Summary: Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $x^2w''+ xw'+ (a^2- x^2)w= 0$. The code also computes exponentially scaled functions. The range of computation is $(x,a)\in (0,1500]\times [-1500, 1500]$ when scaled functions are considered and it is larger than $(0,500]\times [-400, 400]$ for standard IEEE double precision arithmetic. The relative accuracy is better than $10^{-13}$ in the range $(0,200]\times [-200, 200]$ and close to $10^{-12}$ in $(0, 1500]\times [-1500, 1500]$.

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33F05 Numerical approximation of special functions
65Y15 Packaged methods

Keywords: Fortran 77 programs; modified Bessel functions; derivatives

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